Name: eccentric load stresses in structural columns
Uploaded: 2024-05-23T13:00:08.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Physics

PHYS.2

PHYS.2.D

design-of-columns-under-an-eccentric-load

Design of Columns under an Eccentric Load

Für eine Stütze, die mit einer exzentrischen Axiallast in der Symmetrieebene belastet ist, können die Normalspannungen aufgrund der exzentrischen Last als Spannungen aufgrund einer äquivalenten zentrischen Last und Biegung geschrieben werden.
Bei der Konstruktion von Stützen mit exzentrischen Lasten darf die maximale Spannung, die sich in der Stütze entwickelt, die maximal zulässige Spannung nicht überschreiten. Diese Bedingung kann mit zwei unterschiedlichen Ansätzen erfüllt werden.
Bei der Methode der zulässigen Spannung wird davon ausgegangen, dass die zulässige Spannung für die exzentrisch belastete Stütze mit der maximalen Spannung für die mittig belastete Stütze identisch ist. Die zulässige Spannung für die Säule kann als Funktion des Schlankheitsverhältnisses ausgedrückt werden.
Die zulässige Spannung für die zentrische Belastung ist aufgrund des Biegemoments kleiner als die. Dies führt dazu, dass die Methode der zulässigen Belastung zu konservativ ist. 
Zum anderen berücksichtigt das Interaktionsverfahren die zulässige Spannung durch zentrische Belastung und Biegung.
Es enthält eine Gleichung für die maximale Spannung bei zentrischer Belastung, wenn kein Paarmoment vorhanden ist. In ähnlicher Weise definiert es die maximale Spannung durch reine Biegung, wenn keine Belastung vorhanden ist.

bemessung von stützen unter exzentrischer belastung

Die Konstruktion von Stützen, die exzentrischen Belastungen standhalten, ist ein entscheidender Aspekt des Bauingenieurwesens und stellt sicher, dass Strukturen außermittige Belastungen ohne Ausfälle tragen können. Dieser Entwurfsprozess muss die zusätzlichen Normalspannungen berücksichtigen, die durch exzentrische Belastung entstehen und die Spannungsverteilung und Gesamtstabilität einer Stütze erheblich beeinflussen können. Eine exzentrische Last, die auf eine Säule ausgeübt wird, induziert Normalspannungen, die als Kombination von Spannungen aufgrund einer äquivalenten zentrischen Last und zusätzlicher Biegespannungen betrachtet werden können. Dies führt zu einer ungleichmäßigen Spannungsverteilung, die sorgfältig analysiert werden muss, um strukturelles Versagen zu verhindern. Bei der Bemessung von Stützen unter exzentrischen Lasten werden hauptsächlich zwei Methoden eingesetzt: die Methode der zulässigen Spannung und die Methode der Wechselwirkung.

Die Methode der zulässigen Spannung ist ein unkomplizierter Ansatz, bei dem die zulässige Spannung für eine exzentrisch belastete Säule der maximal zulässigen Spannung für eine zentral belastete Säule gleichgesetzt wird. Diese Methode vereinfacht den Entwurfsprozess, indem sie die zulässige Spannung als Funktion des Schlankheitsgrads der Säule behandelt, der ein Maß für ihre Neigung zum Knicken unter Last ist. Bei dieser Methode wird jedoch davon ausgegangen, dass die zulässige Spannung bei zentrischer Belastung die zusätzlichen Spannungen aufgrund der Biegung umfasst, was zu konservativen Konstruktionen führt, die möglicherweise nicht das volle Potenzial des Materials ausschöpfen. Der diesem Ansatz innewohnende Konservatismus gewährleistet die Sicherheit, kann jedoch zu größeren und teureren Säulen als nötig führen.

Die Interaktionsmethode bietet einen differenzierteren Ansatz, indem sie sowohl die zulässigen Spannungen aufgrund zentrischer Belastung als auch die Spannungen aufgrund von Biegemomenten berücksichtigt. Diese Methode bietet einen Rahmen für die Berechnung der maximalen Spannung, der die Säule ohne ein Moment standhalten kann (reine zentrische Belastung) und der maximalen Spannung aufgrund reiner Biegung (ohne axiale Belastung). Durch die gleichzeitige Berücksichtigung dieser Bedingungen ermöglicht die Interaktionsmethode eine genauere und weniger konservative Schätzung der zulässigen Spannungen in exzentrisch belasteten Stützen.

In der Praxis wird die Interaktionsmethode aufgrund ihrer Fähigkeit, Sicherheit und Materialeffizienz in Einklang zu bringen, häufig bevorzugt. Es erfordert eine detaillierte Analyse der Spannungsverteilung innerhalb der Stütze unter Berücksichtigung sowohl axialer Belastungen als auch Biegemomente.

Bemessung von Stützen unter exzentrischer Belastung

Für eine Stütze, die mit einer exzentrischen Axiallast in der Symmetrieebene belastet ist, können die Normalspannungen aufgrund der exzentrischen Belastung als Spannungen aufgrund einer ...

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eccentric load stresses in structural columns

Structural columns under eccentric load must be designed for both axial force and bending stress. An eccentric load is an off-center load, and it creates a non-uniform stress pattern across the column. Engineers must analyze this stress distribution carefully to reduce the risk of failure.

The stress in an eccentrically loaded column can be treated as the sum of two parts. One part comes from an equivalent centric load, which is a load applied through the center of the column. The other part comes from bending stresses caused by the load being off-center.

Two common design approaches are used for these columns. The allowable stress method sets the allowable stress for an eccentrically loaded column equal to the maximum stress allowed for a centrally loaded column. This method uses the column slenderness ratio, which describes how likely a column is to buckle.

The allowable stress method is simple, but it is also conservative. It assumes the centric-load allowable stress already covers the extra bending stress from eccentric loading. As a result, the column may be larger and more expensive than needed, even though the design is safe.

The interaction method gives a more detailed design check. It considers both the allowable stress from centric loading and the stress from bending moment at the same time. It compares the case of pure centric loading, with no couple moment, and the case of pure bending, with no axial load.

Because it includes both effects, the interaction method can estimate allowable stress more accurately. It is often preferred when engineers want a better balance between safety and material use. The method requires careful stress analysis of the column under both axial load and bending moment.

Eccentric Load Stresses in Structural Columns

eccentric-load-stresses-in-structural-columns

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Eccentric loading shows how a column bends when a force is applied off-center. In structural engineering, this matters because the load no longer acts along the centroidal axis, so the column sees both direct compression and bending stress. The off-center force can be treated as two parts. One part is a centric load F that acts along the column’s axis. The other part is a couple moment created by the eccentricity, or distance, between the load and the centroidal axis. To study the column...

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design of columns under an eccentric load

Structural columns under eccentric load must be designed for both axial force and bending stress. An eccentric load is an off-center load, and it creates a non-uniform stress pattern across the column. Engineers must analyze this stress distribution carefully to reduce the risk of failure. The stress in an eccentrically loaded column can be treated as the sum of two parts. One part comes from an equivalent centric load, which is a load applied through the center of the column. The other part...

key terms and concepts

Learn how eccentric loads create combined axial and bending stresses in columns, and compare the allowable stress and interaction methods used in design.

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Eccentric Load Stresses in Structural Columns

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